Problem: Solve for $x$ and $y$ using elimination. ${-4x+3y = -10}$ ${3x-y = 15}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${-4x+3y = -10}$ $9x-3y = 45$ Add the top and bottom equations together. $5x = 35$ $\dfrac{5x}{{5}} = \dfrac{35}{{5}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-4x+3y = -10}\thinspace$ to find $y$ ${-4}{(7)}{ + 3y = -10}$ $-28+3y = -10$ $-28{+28} + 3y = -10{+28}$ $3y = 18$ $\dfrac{3y}{{3}} = \dfrac{18}{{3}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {3x-y = 15}\thinspace$ and get the same answer for $y$ : ${3}{(7)}{ - y = 15}$ ${y = 6}$